Solve the equation. (Find all solutions of the equation in the interval [0, 2pi). Enter your answers as a comma-separated list.)
(3 sin(2x) + 3 cos(2x))^2=9

Answers

Answer 1

I got

[tex]0.75 + 2\pi \times n[/tex]

[tex]5.28 + 2\pi \times n[/tex]

[tex]1 + 2\pi \times n[/tex]

5.53+2pi times n

WORK:

[tex](3 \sin(2x) + 3 \cos(2x) )) {}^{2} = 9[/tex]

[tex] \sin(2x) + \cos(2x) {}^{2} = 3[/tex]

[tex] \sin(x) + \cos(4 {x}^{2} ) = 3[/tex]

[tex]4 {x}^{2} + x = 3[/tex]

[tex]4 {x}^{2} + x - 3 = 0[/tex]

[tex](4x {}^{2} + 4x - 3x - 3 = 0[/tex]

[tex]4x(x + 1) - 3(x + 1) = 0[/tex]

[tex](4x - 3)(x + 1)[/tex]

Solve for x

[tex]4x - 3 = 0[/tex]

[tex]4x = 3[/tex]

[tex]x = \frac{3}{4} [/tex]

[tex]x + 1 = 0[/tex]

[tex]x = - 1[/tex]

While -1 is a solution, it isn't within the interval of 0,2pi.

However, we can use the reference angle identity

[tex] \cos(x) = \cos(x + 2\pi) [/tex]

So some more possible points are

[tex] - 1 + 2\pi[/tex]

Since it on a interval, it must be less than 2 pi or 6.28.

Let find some more points

[tex] - 1 + 2\pi = 5.28[/tex]

So 5.28 is a point,

[tex] \frac{3}{4} + 2\pi = 7.03[/tex]

That is too big since -6.28 is smaller than 7.03

We can use the identity

[tex] \cos(x) = \cos( - x) [/tex]

[tex] \cos( - 1) = \cos( 1 ) [/tex]

1 is smaller than 2pi so it is true.

[tex] \cos( \frac{3}{4} ) = \cos( - \frac{3}{4} ) [/tex]

Negative 3/4 is smaller than zero so it not a solution.

[tex]0.75[/tex]

[tex]5.28[/tex]

[tex] 1[/tex]

Make sure to include

[tex]2\pi \times n[/tex]

so

[tex]0.75 + 2\pi \times n[/tex]

[tex]5.28 + 2\pi \times n[/tex]

[tex]1 + 2\pi \times n[/tex]

We can also -3/4 plus 2 pi.

Which is about 6

5.53.


Related Questions

A rectangle has an area of 170.2m2
One of the sides is 3.7m in length.
Work out the perimeter of the rectangle.​

Answers

Answer:

here

Area = 170.2 M2

Area of rectangle = l *b

let l= 3.7m

170.2 = 3.7* b

b= 46m

now , perimeter = 2(l+b)

= 2( 3.7 + 46)

= 99.4 m

Find the volume please help
(Multiple choice)

Answers

Answer:

A. 72 mi³C. 261.8 mi³

Step-by-step explanation:

Volume formula:

V = 1/3Bh, B- base area, h- height

Q1

V = 1/3*6²*6 = 72 mi³Correct choice is A

Q2

V = 1/3*(π*5²)*10 = 261.8 mi³ (rounded)Correct choice is C

I NEED THIS ASAP

In the diagram below, besides those facts shown, we also have AB = AC. Find the measure of angle A. Please show your work.

Answers

Not sure but try a tutor they help a lot really quick

y= 2x - 1 , y - x = 4​

Answers

Answer:

x=5 and y=9

Step-by-step explanation:

Sub 1 into 2

2x-1 - x = 4

x= 4+1

x= 5

y= 2(5)-1

y= 10-1

y= 9

Find the distance between the points (-7, -10) and (-5, -1)

Answers

Find the Distance Between Two Points
Use the distance formula to determine the distance between two points.
Exact Form:
√85

Decimal Form:
9.21954445

3. Pete is making 8 identical fruit baskets as
gifts. Each basket contains some apples and
12 oranges. Pete uses a total of 168 pieces
of fruit to make the baskets. Determine the
number of apples that are in each basket.

Answers

9 apples per basket

Peter is making 8 identical fruit baskets. If the baskets are identical, that means they all have the same amount of fruit in them. If I know how many apples were used, then I can divide that by the total number of baskets (8) to find out how many apples were used per basket.

12 oranges were used per basket. There were 8 baskets. 12 x 8 = 96, so 96 oranges were used in total.

168 - 96 = 72

There were 72 apples used in total.

There were the same amount of apples in each of the 8 fruit baskets. 72/8 = 9, which means that there were 9 apples per fruit basket.

Please help need to be done quickly

Answers

It’s the last one, D I guess. It’s the square root of the number surrounding x, so it’s going to be the one with the larger numbers

Answer:

13<x<14

Step-by-step explanation:

try using your calculator using square root

i mean square root 169=13 and square root 196=14

area: 45. and one side is 8 feet. what is the missing side? (will give brainlist :D)

Answers

Area = length x width
45sqft = 8ft x W
45/8 = W
5.625 ft = W
The missing side is 5.625 feet

Find the mean absolute deviation (MAD) of the data in the dot plot below.
Mass of each rock
in Ricardo's collection
numbers 35 36 37 38 39 40 41 42 43 44

Answers

Answer: 2 grams

Step-by-step explanation:

Answer:

ANSWER IN THE PHOTO: 2

Giving 12 points, need help urgently

Answers

Answer:

-2 -1 0 1 are the only integer solutions

Answer:

{-2, - 1, 0, 1}

Step-by-step explanation:

The integer solutions will be {-2, - 1, 0, 1}

Make a conjecture. How are rigid transformations and congruent figures related? Check all that apply.
Rigid transformations preserve segment lengths and angle measures.
Rigid transformations produce congruent figures.
If two figures are congruent, then there is a rigid transformation or a combination of rigid transformations that will
map one onto the other.

Answers

Map one onto the other rigid transformations preserve segments

Help ASAP please I would love to recieve it right away

Answers

Answer:

Step-by-step explanation:

LJ/32=13/7 multiplying each side by 32

LJ=32(13)/7

LJ=416/7

LJ=59.4

Fernando has 22 coins consisting of nickels and dimes in his pocket,

The total value of the coins is $1.70
which system of equations can be used to determine the number of
nickels, n, and the number of dimes, d, in his pocket? ANSWER CHOICES IS IN THE PICTURE

Answers

Answer:

the lat one should be the right answer

Step-by-step explanation:

The equation that can be used to represent the situation will be:

0.05n + 0.10d = 1.70n + d = 22

Let the number of nickels be represented by n.

Let the number of dimes be represented by d

Therefore, since Fernando has 22 coins consisting of nickels and dimes in his pocket and the total value of the coins is $1.70.

The equation that can be used to represent the situation will be:

0.05n + 0.10d = 1.70

n + d = 22

Read related link on:

https://brainly.com/question/17360719

Find the slope of the line

Answers

Answer:

the answer is 0

Step-by-step explanation:

Laura had to write 6 pages for a book report. She figured that since it took her an hour to write one-seventh of a page, it will take her 42 hours to complete her book report. Is Laura correct?

Answers

Yes because 6x_____=42 hours

Without looking, Luke picks necklace beads from a bag of 52 beads. Half the beads are rough. The other half are smooth. There are 13 red beads, 13 blue beads, 13 green beads, and 13 black beads.

What is the theoretical probability of selecting a rough bead? Write the probability as a fraction in simplest form.

Answers

Answer:

i

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

26/52 simplifies to 1/2

Guys I need help, if a couch costs 200 dollars and is marked up 300 percent, what is the cost?

Answers

Answer:

200 X 300% =$600.00

Step-by-step explanation:

Help need to know the cross section shape

Answers

Answer:

Step-by-step explanation:

Rectangle

Solve for X

I would really appreciate any help! I need to finish this trigonometry course to graduate.​

Answers

Sorry don’t know I wish I could help on that but I’m dump as you can see

If 12 + 6x is 20 more than 16, what is
the value of 12x?

Answers

Answer:

12x = 48

Step-by-step explanation:

Translating the word problem into an algebraic equation, we have;

12 + 6x = 16 + 20

12 + 6x = 36

6x = 36 - 12

6x = 24

x = 24/6

x = 4

To find 12x;

12x = 12 * 4 = 48

PLEASE HELP. THIS IS WORTH 68 POINTS. FE

Answers

Last option - angle BAF and FAD

Answer:

BAF and FAD

Step-by-step explanation:

Help fast it's worth 20 points if u answer

Answers

Answer: the answer is c

Step-by-step explanation:

Lucas is planting grass on the shaded portions of the yard. What will be the total area covered by​ grass?

Answers

Complete Question:

Lucas is planting grass on the shaded portions of the yard. What will be the total area of covered by grass? Fill in the missing.

Part A= 12 x ? = ? ft²

Part B= 0.5 x ? x 9 = ?ft²

Part C= 0.5 x 7 x ? = ?ft²

Total Area= ?ft²

Answer:

[tex]A = 108ft^2[/tex]

[tex]B = 27ft^2[/tex]

[tex]C = 24.5ft^2[/tex]

[tex]Area = 159.50ft^2[/tex]

Step-by-step explanation:

Given

See attachment

From the attachment;

Part A is a rectangle with dimension 9ft by 12ft

So,

[tex]A = 12ft * 9ft[/tex]

[tex]A = 108ft^2[/tex]

Part B is a triangle with dimension: height = 6 and base = 9

The height is calculated as:

[tex]Height = 12ft - 6ft = 6ft[/tex]

And the base is:

[tex]Base = 18ft - 9ft = 9ft[/tex]

So, the area is:

[tex]B = 0.5 * 6ft * 9ft[/tex]

[tex]B = 27ft^2[/tex]

Part C is a triangle with dimension: height = 7 and base = 7

So, the area is:

[tex]C = 0.5 * 7 * 7ft^2[/tex]

[tex]C = 24.5ft^2[/tex]

Total Area is:

[tex]Area = A + B + C[/tex]

[tex]Area = 108ft^2 + 27ft^2 + 24.5ft^2[/tex]

[tex]Area = 159.50ft^2[/tex]

HELPPPPPP PLEASE I’m confusedddddd

Answers

F I think because of the line and

12(a – 2) = 14 + 3(2b – 1)
5(a + 1) + 2(1 – 2b) = 14
solve with elimantion?

Answers

Answer:

(a,b) = (49/9 , 91/18)

Step-by-step explanation:

12a-6b=35

5a-4b=7

multiply both sides

-24+12b= -70

15a-12b=21

elimiate one varibable by adding the equations  

-9a= -49

divide both sides

a=49/9

subsitite the value of a

5*49/9-4b=7

solve the equation

b=91/18

a possible solution is

(a,b) = (49/9 , 91/18)

Check it if you want but yeah

49/9, 91/8 hope this helps!!

LITERALLY GIVING LIKE 30 POINTS OR WHATEVER IM DESPERATE PLEASE I NEED MODULE 4 NOTES FOR FLVS 8TH GRADE PRE-ALGEBRA?? I HAVE A DBA AND NEED NOTES I BEG ITS FOR MRS. MEURER'S CLASS

Answers

Answer:  While I am not in your class and can not unfortunately specifically help with this I can still give you a basic overview of what you need to know in most pre algebra courses and you can hopefully then use this information in the best way possible.

Step-by-step explanation:  Some of the basic pre algebra concepts include:

Knowing your basic addition, subtraction, multiplication, and division.  I am assuming you know how to do this sort of math.  For example, I mean problems such as 5+4 or 10/5, but if you do need help with these just ask me and I can help you further.

Basic variable usage:  This means being able to solve problems such as x + 10 = 15.  I can help walk you through this sort of problem.  The variable (which is usually represented by the letter x) is used as a placeholder for an unknown number that you need to solve for.  You can think of this more simply in the example I gave as What plus 10 is equal to 15.  That might help you get the basics down if you can think of a problem that way.  As you can probably tell now the answer would be 5.  There may be also more advanced problems regarding variables but not all pre algebra classes will include this material so if you need a review in this you can ask me as well.

Another basic concept is the concept of solving equations.  This can also mean using both addition and multiplication within one equation or things of that nature.  These equations can look something like 18 - (5 + 3^2) + 7 and I can help walk you through a problem like this.  An important fact to remember is the order of operations, which is the way in which you must solve more complex equations like this or if you need to think of it another way it can mean the way you break down an equation.  You probably have heard of PEMDAS before and this is the way you can remember the order of operations.  It is an acronym with each of the letters representing an operation.  P = parenthesis E = exponents M = Multiplication D = division A = addition and S = subtraction.  Now we can use this to solve the equation!  First we should start within the parenthesis so lets only look at that portion of the problem for now to keep things simpler.  Inside the parenthesis it said 5 + 3^2  We see addition and exponents within the parenthesis so because of PEMDAS we should start with the exponent.  Exponents just mean the amount of times you need to multiply the base number by itself.  The base number is the number the exponent is "attached" to.  Our base number is 3 and the exponent is 2 which means we should do the following math 3 * 3 which equals 9  Now we can go back to our original problem inside the parenthesis.  In place of the 3^2 we can instead put 9 now as we know its the answer for that part of the problem.  What we have now is 5 + 9  and we can simply add that to get 14.  This means inside the parenthesis we can replace with just the number 14 as we have already solved everything we need for it.  The equation now looks like --> 18 - (14) + 7.  Now what we have left is addition and subtraction.  Remember on PEMDAS how multiplication and division were next to each other along with addition and subtraction?  For these 4 just because they are next to each other does not dictate the other rather when you are dealing with either just multiplication and division in a problem you work left to right and the same goes for addition and subtraction and since our resulting problem only has addition and subtraction left we will simply just work from the left of the equation to the right.  Our problem as of now is 18 - (14) + 7.  18 - 14 = 4 so we can now have the equation be 4 + 7 and after adding we get our answer which is 11!  I hope you were able to follow along with that and my explanations were satisfactory.

Hopefully at least some of this included in your module 4 but if you would elaborate more I would more than happily assist you more so please do not hesitate to reach out :)

Edit for extra information:

https://rb.gy/qslgfv

If you have anymore questions regarding this information if you would still like me to go over equations with inequalities just let me know!

quick answer please!!!​

Answers

Answer:

a. it has reflectional symmetry with 16 line of symmetry

133 is a whole number. true or false​

Answers

Answer:true

Step-by-step explanation:

the answer will be true :)

3. You invested $11,000 in stocks and bonds paying 5% and 8% annual interest. If the total interest for the year was $730, how much was invested in each account?


4. A California company needs to blend a wine that is 6% alcohol, with a French wine which has a 9% content to obtain 200 gallons with a 7% alcohol content. How much of each kind should he use?

Answers

9514 1404 393

Answer:

  3. $6000 at 8%; $5000 at 5%

  4. 66 2/3 gallons of 9%; 133 1/3 gallons of 6%

Step-by-step explanation:

For many mixture problems, it works well to let a variable represent the amount of the largest contributor used in the mix.

3. Let x represent the amount invested at 8%. Then the total interest is ...

  8%x +5%(11000-x) = 730

  3%x = 730 -550

  x = 180/0.03 = 6000

$6000 was invested at 8%; $5000 was invested at 5%.

__

4. Let x represent the number of gallons of 9% content. Then the alcohol content of the mix is ...

  9%x +6%(200 -x) = 7%(200)

  3%x = 1%(200) . . . . . subtract 6%(200)

  x = 200/3 = 66 2/3 . . . . . divide by 3%

  200 -x = 133 1/3

66 2/3 gallons of 9% wine and 133 1/3 gallons of 6% wine should be used.

ok this is a math question if you don't know anything about this go away.


3. A volleyball coach plans her daily practices to include 10 minutes of stretching, 2/3 of the entire practice scrimmaging, and the remaining practice time working on drills of specific skills. On Wednesday, the coach planned 100 minutes of stretching and scrimmaging. How long, in hours, is the entire practice?

Answers

Answer:h

Step-by-step explanation:

F

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